Is there any prime number p(adsbygoogle = window.adsbygoogle || []).push({}); _{n}, such that it has a relationship with the next prime number p_{n+1}

[tex] p_{n+1} > p_{n}^2 [/tex]

If not, is there any proof saying a prime like this does not exist?

I have the exact same question about this relation:

[tex] p_{n+1} > 2p_{n} [/tex]

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# I Question about the gaps between prime numbers

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